Independence Tests based on Symbolic Dynamics

New methods to test whether a time series is i.i.d. are proposed in a recent series of papers (Matilla-Garcia [2007], Matilla-Garcia and Marin [2008], Matilla-Garcia and Marin [2009], and Matilla-Garcia et al. [2010]). The main idea is to map m-histories of a time series onto elements of the symmetric group. The observed frequencies of the different elements are then used to detect dependencies in the original series. The author will demonstrate that the results presented in the above papers are not correct in the suggested generality. Moreover, simulation results indicate that the performance of the original tests are not as good as betoken.